In many signal processing and machine learning applications, datasets containing private information are held at different locations, requiring the development of distributed privacy-preserving algorithms. Tensor and matrix factorizations are key components of many processing pipelines. In the distributed setting, differentially private algorithms suffer because they introduce noise to guarantee privacy. This paper designs new and improved distributed and differentially private algorithms for two popular matrix and tensor factorization methods: principal component analysis and orthogonal tensor decomposition. The new algorithms employ a correlated noise design scheme to alleviate the effects of noise and can achieve the same noise level as the centralized scenario. Experiments on synthetic and real data illustrate the regimes in which the correlated noise allows performance matching with the centralized setting, outperforming previous methods and demonstrating that meaningful utility is possible while guaranteeing differential privacy.

中文翻译：

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矩阵和张量分解的分布式差分隐私算法

在许多信号处理和机器学习应用中，包含隐私信息的数据集保存在不同的位置，需要开发分布式隐私保护算法。张量和矩阵分解是许多处理流程的关键组成部分。在分布式环境中，差分隐私算法会受到影响，因为它们引入噪声来保证隐私。本文为两种流行的矩阵和张量分解方法设计了新的和改进的分布式差分隐私算法：主成分分析和正交张量分解。新算法采用相关噪声设计方案来减轻噪声的影响，并且可以达到与集中式场景相同的噪声水平。对合成数据和真实数据的实验说明了相关噪声允许与集中设置进行性能匹配的机制，优于以前的方法，并证明在保证差异隐私的同时可以实现有意义的效用。